I guess we've got used to the daily headlines about Jimmy Savile – the BBC, children's homes, Stoke Mandeville and Leeds Hospitals, Broadmoor. Today's headline needs to offer a new angle; a greater number of "lines of inquiry", someone to blame for collusion, for not speaking up, for abusing as well. The work of the police in investigating Savile's crimes (and perhaps those of others) was already complicated. The explosion in allegations as a consequence of these headlines will not have made this task any easier.

Of course Jimmy Savile cannot now be held accountable for his behaviour, so some have asked whether the cost of an expensive police investigation is worthwhile. There is less hesitation about the reviews by the BBC and NHS, where there are clearly a host of lessons to learn – but they can only be learned through thorough independent reviews that need to be prompt but that also allow and encourage honesty. People have made grave mistakes. Some, perhaps many, have turned a blind eye, have blamed the young person, have denied the evidence in front of them, have put self-interest above child protection. Some have not been clear where the legal and moral boundaries lie.

And the consequences have been profound for scores, if not hundreds, of children and young people. On top of the inherent vulnerability of childhood and the additional vulnerabilities that were apparent in the lives of many of those abused, adults around them failed to offer the protection that they had the right to expect. Of course, Jimmy Savile himself must bear the greatest responsibility for the harm done. But so many children could have been protected if bystanders had taken action. Action could have involved the police and social workers. But it should also have involved organisations denying Savile access to children through work and voluntary activities.

Every year thousands of allegations of abuse by workers and volunteers are handled by local authorities and the police. A proportion of confirmed allegations result in serious case reviews: to analyse the circumstances of the abuse, identify shortcomings or failures in policy and practice and, critically, to learn lessons. And there are many lessons to learn. We may not be able to fully extinguish the risk to the most vulnerable in society, but we do have an obligation to take all reasonable steps to avoid repetition of past mistakes.

Last year Nigel Leat, a primary school teacher from North Devon, was sentenced to life in prison for the sexual abuse he inflicted on five primary-aged children in the school where he taught. With all its child protection policies and regular training of staff, the abuse went on for almost 10 years, with lots of school colleagues concerned; a number of allegations sent to the headteacher; questionable sexual material found on school computers and yet little in the way of protection. A remarkably similar state of affairs surrounded the abuse of an unknown number of very young children at Little Ted's Nursery the previous year. This year, Jimmy Savile and Rochdale. And next year?

In the debates about the prevailing culture in the BBC in the 70s and beyond, we must not lose sight of the fact that crimes were committed against children and young people who are carrying the scars to the present day. The wrongdoing may never be prosecuted, but these victims deserve an acknowledgment that harm was done, and that they were in no way to blame. Sexual abuse is as much an abuse of power as anything else. Those with such power – whether by physical strength, position, celebrity, reputation – need to act with respect for and responsibility to those who are more vulnerable. And, as a civilised society, we need to ensure we offer ongoing support and help to those who have suffered abuse – however many years ago. Those organisations that support victims and survivors, often in the voluntary sector and dependent upon grants and donations, need all our support in order to offer the services that their users need.

So we have crimes committed, children harmed, survivors in need of support and help, organisations with lessons to learn (once we know what they are). That was precisely the case before Jimmy Savile, as it will be when the frenzy has died down. At least one in 10 children in the UK experiences sexual abuse before they reach 18, numbers backed up in recent research by the NSPCC. It may be as many as one in six. The only thing that will change that dreadful, shameful statistic is if all adults wake up to the reality of abuse and abusers; choose to learn the signs to look out for in children and adults that might indicate sexual abuse; know where to turn to for advice and support so that they do take action that protects a child.

The Stop it Now! helpline has dealt with over 30,000 calls since it started, with Home Office support, in 2002. Callers agree actions they will take to keep children safe. The Savile case has caused a huge increase in calls – mostly parents concerned about adults involved in their children's lives. Sometimes parents are concerned about sexual behaviour by their children towards other, younger children. Occasionally men are concerned about their own sexual thoughts about children – wanting advice on how to "manage" or "get rid of" these thoughts.

If 30,000 calls result in actions by each caller, then many children will be safer than they might have been. If, then, each adult reading this agrees on action they can take to keep children safe, even more abuse will be prevented. That must surely be a silver lining we can create out of all those gloomy headlines.